Characteristic polynomials of the Hecke operator T2 on Gamma0(5) for weights up to 48

Level 5, Rational newforms page

{4, 4 + x}

{6, -2 + x}

{8, (14 + x)*(24 - 20*x + x^2)}

{10, (8 + x)*(-984 + 10*x + x^2)}

{12, (-34 + x)*(-5336 + 20*x + x^2)}

{14, (-6384 + 80*x + x^2)*(901248 - 11144*x - 142*x^2 + x^3)}

{16, (-4496 + 310*x + x^2)*(-5408256 - 59336*x - 4*x^2 + x^3)}

{18, (65056 - 680*x + x^2)*(-8070528 - 198104*x - 118*x^2 + x^3)}

{20, (-578651136 - 757856*x + 1006*x^2 + x^3)* (237314973696 - 746347520*x - 2002872*x^2 + 420*x^3 + x^4)}

{22, (-2939762688 - 2780624*x + 1312*x^2 + x^3)* (-4309053579264 + 15642931840*x - 4542888*x^2 - 2910*x^3 + x^4)}

{24, (5728572416 - 7619376*x - 666*x^2 + x^3)* (38396524609536 + 16729054720*x - 22815912*x^2 + 780*x^3 + x^4)}

{26, (2578152318959616 - 20279449600*x - 113135808*x^2 - 600*x^3 + x^4)* (3498510988641042432 + 2127699725500416*x - 367856402816*x^2 - 118822008*x^3 + 4602*x^4 + x^5)}

{28, (-5427025739710464 - 3942345932800*x - 381050112*x^2 + 11550*x^3 + x^4)*(-12783803780642635776 + 6144845117710336*x + 4473573947392*x^2 - 262965912*x^3 - 19916*x^4 + x^5)}

{30, (185821106961186816 - 10172141670400*x - 1488850608*x^2 + 15600*x^3 + x^4)*(-6894155114841932562432 + 1029423429856239616*x + 19813190809216*x^2 - 2124404808*x^3 - 14702*x^4 + x^5)}

{32, (16285145847385055821824 + 5619250047765446656*x + 109558719721472*x^2 - 6463342032*x^3 - 13546*x^4 + x^5)* (-11874850129281021672261943296 + 660624932299539166003200*x + 14074549466193952768*x^2 - 597605067046400*x^3 - 9717523848*x^4 + 60700*x^5 + x^6)}

{34, (-405031639619030621356032 + 70175438451212025856*x + 440682607210496*x^2 - 21581220768*x^3 - 30472*x^4 + x^5)* (-403252523683384760678328827904 - 18902755381238535133593600*x + 248434013984696762368*x^2 + 3571811788892800*x^3 - 29674115352*x^4 - 147350*x^5 + x^6)}

{36, (158619773841088624906469376 - 361719193835975081984*x - 22892027716774912*x^2 - 22753970592*x^3 + 459086*x^4 + x^5)* (-16665395334787583567211094081536 - 487645666517514099831603200*x + 6162882801961475022848*x^2 + 9806582535654400*x^3 - 156014221688*x^4 - 48700*x^5 + x^6)}

{38, (-2927531696552673396483309818609664 - 23054098974465672802562211840*x + 80802274627520994869248*x^2 + 257287962497054720*x^3 - 599977421712*x^4 - 485440*x^5 + x^6)* (135469544210541630436777601455953543168 - 2430014237790356648510477863747584*x - 18016367649275949875216777216*x^2 + 122144709718595480772608*x^3 + 125865094100404864*x^4 - 710300531432*x^5 - 165502*x^6 + x^7)}

{40, (-98732317125225293301783655933280256 + 434222363394194178099925483520*x + 1581626603027679982911488*x^2 - 518463748218250240*x^3 - 2617302762608*x^4 + 86470*x^5 + x^6)* (-11968763128612851920767490357097362620416 - 310472711097123198471869546455105536*x + 448262713402924995286493298688*x^2 + 2110962859795661029326848*x^3 - 1163519423942793728*x^4 - 2914991491688*x^5 + 486956*x^6 + x^7)}

{42, (-566799467436845771666221049875267584 + 2636404056426918216165113200640*x + 742062623409594412433408*x^2 - 9345568987611473920*x^3 - 4018315989632*x^4 + 2330440*x^5 + x^6)* (21458377566960183246390899719689370916093952 - 12278311612966954054760112377774997504*x - 36055614393310787793349964201984*x^2 + 20043946076021381348999168*x^3 + 17345789505997096576*x^4 - 9365334208952*x^5 - 1971238*x^6 + x^7)}

{44, (233998597228496691958924597600664440887312384 - 999061125922107782893695062606019035136*x - 129194235789278816206352350707712*x^2 + 447797695952419961585205248*x^3 + 1415392134078543872*x^4 - 40429075239488*x^5 + 110206*x^6 + x^7)* (6459836136070389145672685470128855662444675843751936 + 5757446604961207918636919148201013099616010240*x - 5489264111056822328511677191166502109184*x^2 - 1482097024340196603335633975377920*x^3 + 993906702059247827518119936*x^4 + 121970282341031813120*x^5 - 58342530047064*x^6 - 2432940*x^7 + x^8)}

{46, (-101598487886568124803899865552602632404942716928 - 112831975749487600091679603643114768564224*x - 16021606352446724565279057519837184*x^2 + 9756109470565320940842057728*x^3 + 448758614082393890816*x^4 - 186692916290672*x^5 - 2914928*x^6 + x^7)* (-1156911298365033632422710148489185328078721233604050944 - 807714989514479557053567054665416547396097146880*x + 3998169968001431395614258527795616415744*x^2 + 86649740262003850296009611186012160*x^3 + 11122405592570497753236381696*x^4 - 1435010426196994503040*x^5 - 215170941620616*x^6 + 6349170*x^7 + x^8)}

{48, (17527645858509780693920203852777540811803701805056 - 8389903079302863661689967152522012032761856*x + 435113539440451252023949546500390912*x^2 + 143687854676401999304281817088*x^3 - 5158077730030203348992*x^4 - 680860469710608*x^5 + 11622774*x^6 + x^7)* (375406123953833149148234409053475993939397971370989060096 + 22082424842601470824425819735109316321963315036160*x - 14682060103716211421989009510787794929188864*x^2 - 710804190082676929028810733602734080*x^3 + 167205863109594852465146658816*x^4 + 4976532290434395015680*x^5 - 731973355844424*x^6 - 8440260*x^7 + x^8)}